Contour integral with delta function

[mhill]

Using Cauchy's integral theorem how could we compute

\oint _{C}dz D^{r} \delta (z) z^{-m}

since delta (z) is not strictly an analytic function and we have a pole of order 'm' here C is a closed contour in complex plane

 

[Santa1]

Can you find out for which z there is a pole?

If so, can you recall what Cauchy's integral theorem states?

 

[matt grime]

When you write 'isn't strictly analytic' you are implying (to me at least) it is really close to being one. It isn't even a function of a complex variable.

Should you want to do this for any reason, then why not try the normal limit via a sequence of functions that converge to the delta distribution?

 

[jostpuur]

What kind of path is the C. Does it go through origo? If the integration path does not intersect the origo, isn't the integral zero because integrand is zero along the path? If the integration path intersects the origo, isn't it a divergent integral then?

What does D^r mean? Is it a constant, or a derivative operator?